Should the phone identify those things and automatically blur out all of the sensitive information in those photos too?
I’d prefer if my phone did neither that nor told the apps that a screenshot was being taken nor allowing the apps to hide anything that was on screen when a screenshot is taken.
It’s my phone, I want to decide what I take photos and screenshots of.
That's the crux.
Yes, it is unreasonable, because scams have proven to be just as effective at getting people to just read the details out over the phone line, and bank these days are not showing much sensitive information in the open anyways (my recent annoyance - someone thought it's a good idea to never show the full account number on screen, showing just first and last few digits, and an option to copy to clipboard...).
Meanwhile, those very apps tend to be ones people would most often want to screenshot for legitimate reasons - e.g. to communicate or make a record of specific transactions, accounts, their states, metadata, etc. None of which is copyable text in the app, and most of it isn't even properly exportable, so it's not like there's any other way.
Done.
Just do a security alert pop up "You are screenshotting potentially sensitive information, are you sure you want to continue".
The same can be said wrt people being too careless to have their car/bike/etc. Or powertools.
In any of those cases, just try take them away and see how that goes…
Imagine having to type "I want to get hacked" on a keyboard layout which randomizes with every character.
It's not like computers give people a good reason to read the error popups. 90% of them these days are just "oops, computer pooped itself, a well trained army of monkeys is on its way to clean it up; try again later <tinyprint>0xbunchofbullshit-hexadecimal-uuids-for-vendor-telemetry</tinyprint> ;-)" anyway.
Most of the time, people are given only two options: give up on their task, or ignore the popup. No point in reading the message in such cases, it brings zero value.
Repeated exposure built immunity.
You get a scary error with incomprehensible details[1], maybe the app closes, so you open it again and continue until the next error happens; maybe it doesn't close, just keeps going - maybe partially broken, maybe not. Either way, text is incomprehensible, but dismissing the message lets you keep going, so you learn that. At some point you see the message, think "oh this again", and close it without thinking. Works 90% of the time, for the other 10% you have coping strategies like "press CTRL+S every 30 seconds", "use Save As instead of save", or "make a copy of the file at start of your work session" all committed to muscle memory.
The modals with two or more buttons were the annoying ones. Asking you to make a decision. Asking you to stop. Eventually you learned to press the right button for ones where it mattered, and go straight for [X] or "Cancel" for everything else. And it worked.
Then came the web, and that's a rant for another time, but suffice it to say, the advertisers successfully taught everyone that you should always click the "X" button on anything that pops up without reading it, way before web apps became a thing.
We've worked out some useful UX patterns since. Non-blocking notifications, side panes, undo, undo history (still annoyingly uncommon). I don't think there's a single solution to the problem, but I am sure of the underlying principle that should guide it:
Whatever you do, do not become an obstacle standing between the user and the thing they're trying to do.
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[0] - Can't speak for the kids these days, who learned computers after Windows ME times, or just grew straight into mobile revolution and mostly skipped dealing with PCs.
[1] - That was bad, but we've since overcorrected in the opposite direction. Ideal is IMO enough information to give you a clue about internal and external causes and state of the program, even if you have no technical background, because people bent on doing a task and even minimally curious can use that to random-walk into a solution. Basically: something you can act on as a user if you really care to.